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Elsevier, Journal of Combinatorial Theory, Series A, 2(72), p. 340-344, 1995

DOI: 10.1016/0097-3165(95)90073-x

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Approximating fair division with a limited number of cuts

Journal article published in 1995 by Jack M. Robertson, William A. Webb
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

A large class A of finite algorithms for fairly dividing a cake using k of fewer cuts is described. Assume an algorithm assigns piece Xi to player Pi using associated probability measure μi on measurable subsets of the cake X. If M(n, k) = max mini(μi(Xi)) and N(n, k) = max(number of i such that ) then for , for n ⩾ 3, , and for n ⩾ 4, . Also N(2n − 2, n − 1) = n.